1. Field of the Invention:
The inventive concept relates to the field of measurement of volume changes in dry particulate systems in triaxial testers.
2. Description of the Prior Art
It is not an exaggeration to say that particles impact every aspect of our modern lives. They are found in our food, aerosols, cements, cosmetic preparations, drug preparations, dyes etc. All industries deal with particles at one point or another; examples being chemical, pharmaceutical, food and mining, to name a few. The importance of particle chemistry and behavior cannot be overstressed. In the past 30 years, the measurement of flow properties of particulate systems has received considerable interest in powder technology. The study of powder flow has evolved into the new field of powder mechanics; however, this field is still in its infancy due to the complex nature of powder flow. The present invention focuses on one of the tools that is available to study powder flow, namely, an enhanced triaxial tester.
Following is a brief comparative survey of conventional flow testers, their classification, and several techniques for the determination of volume change.
There are many different kinds of flow testers that are commercially available, which allow the determination of some measure of flowability. Examples are, but not limited to, Jenike's shear cell, annular shear cells, Hosokawa tester, Johanson Indicizers, and uniaxial tester. There are a few other flow testers that are used for research purposes and are owned by a handful of research institutions worldwide, such as the biaxial tester, and true triaxial tester. These testers are extremely complicated to build and to operate and they haven't been developed to a stage of practical utility. A true triaxial tester can cost over half a million dollars. Many of the commercially available devices are very empirical in nature and the flow parameters obtained are based on assumptions that do not have a solid scientific foundation. Moreover, they don't provide enough information for the formulation of a general 3-dimensional constitutive model. In addition most of these devices test powder already in flow or no-flow but are unable to determine the conditions when the powder is partially in flow and partially in no-flow. An extensive review of these testers can be found in van der Kraan, [“Techniques for the Measurement of Flow properties of Cohesive Powders”, Copy Print 2000, Enschede (1996)] and Schwedes, [“Testers for measuring Flow Properties of particulate Solids”, Proceedings Reliable Flow of Particulate Solids III, P{orsagrunn, Norway, pp. 3–40 (August, 1999)]. See also, Cazacu, et al, “A New Constitutive Modelfor Alumina Powder Compaction,” 103–112, No. 15; Cristescu, “Recent Developments on Computer Modeling of Powder Metallurgy Operations,” keynote lecture at NATO Advanced Research Workshop, May 15–18, 2000 Kiev, Ukraine; Cristescu, et al, “Constitutive equation for compaction of ceramic powders,” IUTAM Symposium on Mechanics of Granular and Porous materials, 117–128, (1997) Kluwer Academic Publishers, and Jin, et al, “A Constitutive Model for Powder Materials,” Journal of Engineering Materials and Technology. 1–8, vol. 120 (1998).
The triaxial tester is another tester that could be potentially useful as a powder flow tester, however in its currently available form it is not suitable for the study of dry cohesive powders. The present invention is concerned with an enhancement of the triaxial cell, which is an indirect shear tester. The classical triaxial cell (FIG. 1) was invented about a century ago for the purpose of characterizing soil behavior over a range of pressures that is of interest in civil engineering and mining applications. See, e.g., U.S. Pat. No. 4,502,338. Most of the triaxial shear testing equipment uses the specimen in a wetted or saturated form; however, this might interfere with, or change the inherent properties of the powder. In addition they are primarily designed to operate under elevated pressures that are applicable to geomechanics. This motivated the development of the dry system and the volume change device applicable to low confining pressures.
The testers fall into two main categories, i.e., direct and indirect shear testers. In direct shear testers the location of the shear zone or shear plane is determined by the design of the tester, whereas in indirect shear testers the powder develops its own shear plane or shear zone before failure due to its state of stress.
There are three principal methods that can be used to measure volume change [see Bishop and Henkel, “The Measurement of Soil Properties in the Triaxial Test”, Edward Arnold LTD, London (1957)]: (a) by measuring the volume of fluid entering the cell (when the specimen is compressing) or leaving the cell (when the specimen is dilating), (b) by measuring the volume of fluid entering or leaving the interstitial space (or pore space) of the soil, (c) by the direct measurement of the change in length and diameter of the specimen. Methods (b) and (c) are not applicable to dry powders. Method (b) is not applicable because the sample is dry, therefore no fluid can be introduced, and moreover air, being compressible, is not a good candidate for volume measurements. Method (c) is highly inaccurate at very low confining pressures because the pressure exerted by the mechanical device on the specimen for measuring the diameter change is of the same order of magnitude as the confining pressure.
There are several devices available for measuring volume change under pressure. The first one is a self-compensating U-tube in which mercury is used to provide pressure. A spring is attached to one side of the U-tube to compensate for the head resulting from the displacement of the mercury. The accuracy of such devices is about 0.01% of the initial volume of the sample, i.e., about 0.06 cm3. If regulated air supply is available, the direct burette or bellows techniques can be alternatively considered. In the direct burette technique, connections are made from the cell to the burette, which is partially filled with fluid and confining air pressure is directly applied to the top of the fluid. The accuracy of this method is about 0.05 cm3. All of the above methods require manual operation and are not suitable for automation or on-line monitoring of the volume change. There is an enhanced version of the direct burette method which utilizes a float, placed on top of the fluid in the burette, with a rod that forms a push rod of an LVDT (linear variable differential transducer) for computerized data acquisition. The bellows based technique uses bellows as the name suggests which is connected to an LVDT. The bellows expand and contract proportionally to the volume change and the LVDT provides the input data for automation. The accuracy of the new volume change device is about 0.005% of the initial volume, which translates to about 0.009 cm3. The accuracy of the volume measurements is about an order of magnitude better than that of currently existing devices.
As one focuses on smaller particle sizes at the micro level, or as confining loads decrease, the influence of interparticle cohesive forces increases. The potential for significant volume change upon shearing can be much greater for particles with significant cohesion since such particles can form loose networks of contacts which can move as rigid bodies and cause dilation of the bulk material or, can collapse to denser configurations. These volume changes can be quite large and can occur at very short periods of time. As a result, the conventional volume change devices described above are unable to capture such events. Thus, there is a critical need for developing techniques that are suitable for characterizing such systems. A few researchers have developed equipment capable of measuring the biaxial and triaxial response of dry samples. Van der Kraan, supra, describes a technique for measuring the volume change of dry powder systems. Using this technique, a series of triaxial compression tests on alumina powder (mean particle size 100 gm) have been carried out under a confining pressure of 9.7 KPa (1.4 psi) and 16 KPa (2.3 psi) respectively using a conventional triaxial compression cell. A set of hydrostatic tests followed by triaxial compression tests was done on microcrystalline cellulose (mean particle size 20 gm). The main features of the behavior have been captured with improved accuracy. The equipment enhancements represent technological advances that allow more accurate measurements over a wider range of stresses and strains and volumetric deformations that can be explored utilizing other prior art systems and techniques.
None of the powder flow testers presently available are equipped with a device capable of automatic volume change sensing. Moreover, the operating principles on which these devices rely inhibit the use of any volumetric change device. Examples of commercially available systems are the Johanson Indicizer described in U.S. Pat. No. 4,715,212 and the computer control shear cell tester described in U.S. Pat. No. 6,003,382, both of which are examples of the direct shear testers discussed above. Other typical prior art triaxial testers are described in U.S. Pat. Nos. 4,679,441; 5,265,461; 5,435,187; 6,247,358; 4,579,003; 5,025,668 and 5,159,828. The entire contents and disclosures of all U.S. patents named herein are incorporated herein by reference.
Some of the triaxial testing devices employed by civil engineers are equipped with a volume change device; however, these volume change devices have been designed to operate without significant errors at elevated pressures which are encountered in geomechanics. None of these devices are applicable to measure volume change in dry particulate systems at low confining pressures.